Multiplicity Results of Solutions to the Double Phase Problems of Schrödinger–Kirchhoff Type with Concave–Convex Nonlinearities

Yun-Ho Kim () and Taek-Jun Jeong
Additional contact information
Yun-Ho Kim: Department of Mathematics Education, Sangmyung University, Seoul 03016, Republic of Korea
Taek-Jun Jeong: Department of Mathematics Education, Sangmyung University, Seoul 03016, Republic of Korea

Mathematics, 2023, vol. 12, issue 1, 1-35

Abstract: The present paper is devoted to establishing several existence results for infinitely many solutions to Schrödinger–Kirchhoff-type double phase problems with concave–convex nonlinearities. The first aim is to demonstrate the existence of a sequence of infinitely many large-energy solutions by applying the fountain theorem as the main tool. The second aim is to obtain that our problem admits a sequence of infinitely many small-energy solutions. To obtain these results, we utilize the dual fountain theorem. In addition, we prove the existence of a sequence of infinitely many weak solutions converging to 0 in L ∞ -space. To derive this result, we exploit the dual fountain theorem and the modified functional method.

Keywords: Kirchhoff function; double phase problems; Musielak–Orlicz–Sobolev spaces; multiple solutions; variational methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/1/60/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/1/60/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2023:i:1:p:60-:d:1306663

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().